U.S. patent number 7,630,871 [Application Number 10/931,273] was granted by the patent office on 2009-12-08 for crush modelling.
This patent grant is currently assigned to Engenuity Limited. Invention is credited to James Anderson, Graham Barnes, Ian Cole, Richard Roberts.
United States Patent |
7,630,871 |
Cole , et al. |
December 8, 2009 |
Crush modelling
Abstract
A method of determining the impact resistance of a structure
including a crushable material comprises the steps of determining
for one or more layers of a finite element of said material during
an impact whether said element or layer thereof is to be treated as
failing by crushing. If the element or layer is determined to fail
by crushing, a load-bearing portion of the structure is defined and
the load-bearing portion is treated for the purpose of subsequent
calculations as exhibiting an ongoing resistance.
Inventors: |
Cole; Ian (Sompting,
GB), Barnes; Graham (Dormansland Lingfield,
GB), Roberts; Richard (Henfield, GB),
Anderson; James (Brighton, GB) |
Assignee: |
Engenuity Limited (West Sussex,
GB)
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Family
ID: |
32843561 |
Appl.
No.: |
10/931,273 |
Filed: |
August 31, 2004 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20060004550 A1 |
Jan 5, 2006 |
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Foreign Application Priority Data
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Jul 2, 2004 [GB] |
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0414992.8 |
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Current U.S.
Class: |
703/8; 703/7;
703/2; 700/98; 700/146 |
Current CPC
Class: |
G06F
30/23 (20200101); G06F 30/15 (20200101); G06F
2113/26 (20200101) |
Current International
Class: |
G06F
7/60 (20060101); G06F 19/00 (20060101); G06G
7/48 (20060101) |
Field of
Search: |
;703/8,2,7
;364/472,578 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Mamalis et al. "Crushing of Hybrid Square Sandwich Composite
Vehicle Hollow Bodyshells with Reinforced Core Subjected to Axial
Loading: Numerical Simulation" May 2003. Composite Structures:
175-186. cited by examiner .
Johnson et al. "Computational Methods for Predicting Impact Damage
in Composite Structures". Composites Science and Technology 2001:
2183-2192. cited by examiner .
"LS-DYNA User's Manual: Nonlinear Dynamic Analysis of Structures"
May 1999. cited by examiner .
Palazotto et al. "Finite Element Analysis of Low-Velocity Impact on
Composite Sandwich Plates" 2000. cited by examiner .
MSC.Dytran "User's Manual" Version 4.7: 1997. pp. 1-1, 1-2,
2-20:2-22. cited by examiner .
Belingardi et al. "Numerical Simulation of Fragmentation of
Composite Material Plates Due to Impact" Int. J. Impact Engng vol.
21, No. 5: 1998. cited by examiner .
Christoforou, Andreas. "Impact Dynamics and Damage in Composite
Structures" Composite Structures 2001. cited by examiner .
Johnson, et al. "Computational Methods for Predicting Impact Damage
in Composite Structures", Composites Science and Technology, 2001.
cited by examiner .
Li, et al. "Low-Velocity Impact-Induced Damage of Continuous
Fiber-Reinforced Composite Laminates. Part I. An FEM Numerical
Model", Composites: Part A 2002. cited by examiner .
K. Schweizerhof et al., "Composite crash elements for energy
absorption in frontal crash situations," VDI Report No. 1007, pp.
523-545, 1992 (with translation). cited by other.
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Primary Examiner: Shah; Kamini S
Assistant Examiner: Patel; Shambhavi
Attorney, Agent or Firm: Ohlandt, Greeley, Ruggiero &
Perle, L.L.P.
Claims
The invention claimed is:
1. A method of modelling the behaviour of a structure during an
impact, said structure incorporating a material which can fail
through a crush failure mode whereby said material is continuously
consumed in a crush direction by disintegrating into debris, the
method comprising the steps of determining for one or more layers
of a finite element of said material during said impact whether
said element or layer thereof is failing by said crush failure
mode; and if said element or layer is determined to be failing by
said crush failure mode, defining a crush front or barrier and
allowing the element or layer to pass through said crush front or
barrier whilst being crushed, and assigning to a portion of the
structure an ongoing resistance in the crush direction as the
element or layer passes through the barrier, and using said model
to output data from which a predicted impact resistance of said
structure can be calculated.
2. A method as claimed in claim 1 wherein said portion comprises a
portion of said element or layer.
3. A method as claimed in claim 2 comprising applying said ongoing
resistance to individual nodes of the element or layer so that said
portion comprises said nodes.
4. A method as claimed in claim 3 comprising: defining a crush
front or barrier and allowing said element or layer to pass through
said crush front or barrier whilst being crushed; and dividing said
ongoing resistance by allocating a first percentage of said ongoing
resistance to a first set of nodes that have passed through the
crush front or barrier and a second percentage of said ongoing
resistance to a second set of nodes that have not passed through
the crush front or barrier, wherein said first and second
percentages are calculated either as a function of the area of the
element or layer that has passed through the crush front or barrier
or as a function of the distance that said element or layer has
passed through the crush front or barrier.
5. A method as claimed in claim 4 wherein said first percentage is
the percentage of the area of the element or layer that has passed
through the crush front or barrier or the percentage of the length
of the element or layer normal to the crush front or barrier that
has passed through the crush front or barrier.
6. A method as claimed in claim 1 comprising determining whether
the element or layer is failing by said crush failure mode by
determining whether an impactor barrier has physically encroached
into a space allocated to said element or layer.
7. A method as claimed in claim 1 comprising determining whether
the element or layer is failing by said crush failure mode by
calculating the stress or strain on the element or layer and
comparing said stress or strain with a threshold failure value.
8. A method as claimed in claim 1 comprising defining a crush front
or barrier and determining said ongoing resistance as a function of
a thickness of the element or layer being crushed along the crush
front or barrier.
9. A method as claimed in claim 1 comprising defining a crush front
or barrier and determining said ongoing resistance as a function of
an area of contact at the crush front or barrier.
10. A method as claimed in claim 9 wherein for a given element said
ongoing resistance has an actual value which is a constant function
of the area of contact.
11. A method as claimed in claim 10 comprising defining said
ongoing resistance force as being directly proportional to the area
of contact.
12. A method as claimed in claim 1 wherein said crushable material
is a composite material having a plurality of layers, the method
comprising determining said resistance as a function of the lay-up
of said layers.
13. A method as claimed in claim 12 comprising determining said
resistance as a function of the order of said layers in the
composite.
14. A method as claimed in claim 1 comprising determining said
ongoing resistance as a function of one or more dynamic parameters
relating to the impact.
15. A method as claimed in claim 14 comprising determining said
ongoing resistance as a function of a velocity and/or an angle at
which said element or layer is struck.
16. A method as claimed in claim 14 comprising determining said
ongoing resistance as a function of an amount of rotation imparted
to the element or layer.
17. A method as claimed in claim 1 comprising the step of
designating a set of finite elements of the structure as being
susceptible to failure by said crush failure mode.
18. A method as claimed in claim 17 wherein said set is only a
subset of all available elements.
19. A method as claimed in claim 1 further comprising carrying out
finite element calculations on said element or layer in addition to
assigning said ongoing resistance to said portion and using the
results calculated by said finite element calculations in
subsequent analysis instead of said ongoing resistance if said
results indicate the element or layer is not failing by said crush
failure mode.
20. A method as claimed in claim 19 comprising allocating an
element a degraded crush capability for future crush analysis if
the results calculated by said finite element analysis are
used.
21. A method as claimed in claim 1 wherein said finite elements are
shell elements.
22. A method as claimed in claim 1 wherein said finite elements are
solid elements.
23. A method as claimed in claim 1 wherein said finite elements are
beam elements.
24. A method as claimed in claim 1 comprising defining a crush
front or barrier and adjusting a relative velocity between an
impactor and said element or layer during passage of the crush
front or barrier through the element.
25. A method as claimed in claim 24 comprising modifying the
ongoing resistance along a length of the element in accordance with
a predetermined function of the relative velocity.
26. A method as claimed in claim 1 comprising defining a crush
front or barrier and adjusting an angle of impact between an
impactor and said element or layer during passage of the crush
front or barrier through the element.
27. A method as claimed in claim 26 comprising modifying the
ongoing resistance along a length of the element in accordance with
a predetermined function of the angle of impact.
28. A method as claimed in claim 1 comprising defining a crush
front or barrier and specifying a friction of the element or layer
with the crush front or barrier.
29. A method as claimed in claim 1 comprising specifying material
damping coefficients.
30. A method as claimed in claim 1 wherein said crushable material
comprises a composite material.
31. A method as claimed in claim 30 wherein said composite material
is a fiber-reinforced composite material.
32. A method as claimed in claim 30 wherein said composite material
is a carbon-fiber reinforced resin.
33. A method of modelling the behaviour of a structure during an
impact, said structure incorporating a material which can fail
through a crush failure mode whereby said material is continuously
consumed in a crush direction by disintegrating into debris, the
method comprising the steps of determining for one or more layers
of a finite element of said material during an impact whether said
element or layer thereof is failing by said crush failure mode; and
if said element or layer is determined to be failing by said crush
failure mode, defining a crush front or barrier and allowing the
element or layer to pass through said crush front or barrier whilst
being crushed, and calculating a resistance force and assigning
said resistance force to said element or layer, wherein said steps
of calculating and applying are carried out one or more times such
that a resistance force is assigned to a portion of the structure
in the crush direction as said element or layer passes through said
barrier; and using said model to output data from which a predicted
impact resistance of said structure can be calculated.
34. Computer software which, when executed on suitable data
processing means, models the behaviour of a structure during an
impact, said structure incorporating a material which can fail
through a crush failure mode whereby said material is continuously
consumed in a crush direction by disintegrating into debris, said
software determining for one or more layers of a finite element of
said material during said impact whether said element or layer
thereof is failing by said crush failure mode and if said element
is determined to be failing by said crush failure mode, defining a
crush front or barrier and allowing the element or layer to pass
through said crush front or barrier whilst being crushed, and
assigning to a portion of the structure an ongoing resistance in
the crush direction as the element or layer passes through the
barrier, and using said model to output data from which a predicted
impact resistance of said structure can be calculated.
35. Software for performing finite element modelling comprising
software as claimed in claim 34.
36. Software as claimed in claim 35 wherein said finite element
modelling is non-linear.
37. Software as claimed in claim 35 wherein said finite element
modelling is explicit non-linear.
38. A data processing system which models the behaviour of a
structure during an impact comprising: a computer that: (i)
determines for one or more layers of a finite element of a material
during said impact whether said element or layer thereof is failing
by a crush failure mode whereby said material is continuously
consumed in a crush direction by disintegrating into debris; (ii)
if said element is determined to be failing by said crush failure
mode pursuant to (i) above, said computer defines a crush front or
barrier and allows the element or layer to pass through said crush
front or barrier whilst being crushed, and assigns to a portion of
said structure an ongoing resistance in the crush direction as the
element or layer passes through the barrier; and (iii) using said
model to output data from which a predicted impact resistance of
said structure can be calculated.
39. A method of modelling the behaviour of a structure during an
impact, said structure incorporating a material which can fail
through a crush failure mode whereby said material is continuously
consumed in a crush direction by disintegrating into debris, the
method comprising the steps of using a computer to determine for
one or more layers of a finite element of said material during said
impact whether said element or layer thereof is failing by said
crush failure mode; and if said element or layer is determined to
be failing by said crush failure mode, defining a crush front or
barrier and allowing the element or layer to pass through said
crush front or barrier whilst being crushed, and assigning to a
portion of the structure an ongoing resistance in the crush
direction as the element or layer passes through the barrier, and
outputting data from which the predicted impact resistance of said
structure can be calculated.
Description
FIELD OF THE INVENTION
This invention relates to methods, apparatus and software for
modelling the behaviour of materials which are crushed
particularly, but not exclusively, in the context of composite
vehicle body parts under impact.
BACKGROUND
It has been recognised for a long time that fiber-reinforced
composite materials, particularly carbon fiber composites have
great potential for revolutionising the auto industry. It is well
known that composites are very light compared to their metal
equivalents, even aluminium, and can be formed into complex shapes
that can do the same job as many welded metal stampings.
Composites also have the ability to absorb high amounts of energy
during impacts which make them ideal for automotive, rail or civil
applications. For example, whereas steel can only absorb up to 20
kilojoules per kilogramme and aluminium approximately 30 kilojoules
per kilogramme, carbon composites can absorb up to 80 kilojoules
per kilogramme.
In addition, unlike metallic structures, the crushed material has
very little residual strength after it has absorbed the energy.
Instead, the composite material is essentially transformed into
small pieces of debris and loosely connected fibres after it has
been crushed which means that less space is required than in an
equivalent metal structure. This is because in a metal structure
space must be provided in designated crumple zones to accommodate
the buckled metal.
There is, therefore, a significant incentive to using composite
materials such as carbon fiber composites in mass production
vehicles. However, to date they have only been used in very limited
applications such as top-end sports cars, motor sport and small,
non-critical parts of mass produced cars.
Two significant current disadvantages of composites is that they
are relatively costly and have long manufacturing cycle times.
However, a significant barrier which still remains to their
widespread use in the automotive industry is the ability to be able
to model their performance in an impact. This is of course
essential to be able to do in order to design vehicles which are as
safe as possible and which will behave in a predictable way in the
event of a crash. Although crash performance testing can be carried
out by building prototypes, this is extremely expensive and is only
practically feasible in the latter stages of design to prove the
basic design and calibrate restraint systems. During the earlier
stages of design of vehicles made from metal, finite element
analysis is used to model the behaviour and interaction of the
various metal parts and to predict their performance in the event
of an impact. This means that designs can be proposed, tested and
modified using computer modelling with much less reliance on
producing and testing expensive prototypes.
However, this approach does not currently work for crushable
materials such as composites. The reason for this is that
composites absorb energy by a very different mechanism to metallic
structures. Metallic structures absorb energy by plastic folding of
the metal, initiated by local buckling of the material, which can
be characterised by a stress vs strain curve to good effect. At
limit, final failure, which may be tearing or brittle fracture,
results in the element being unable to transfer load, although its
initial volume is essential unchanged.
On the microscopic scale however some materials such as composites
absorb energy by local crushing of the material, by matrix
cracking, fiber buckling and fracture, frictional heating etc.
Viewed on a macro scale, the material is essentially crushed or
consumed by the impact on a continuous basis, and the volume of the
material is reduced as the structural material is turned to
debris.
It is widely recognised in the art that no satisfactory way of
modelling the crush performance of composite materials exists.
Existing finite element analysis techniques tend to treat elements
of composite by treating the whole element or separate layers
thereof as maintaining their integrity until the appropriate
failure stress value is reached, whereafter the element or layer is
simply deleted from the analysis or the element or layer is deleted
from the analysis in a predefined period. In a typical example,
this might result in the element being deleted with only 5% of its
original edge length compressed. The conventional finite element
calculations essentially cannot deal with very large changes in
volume and therefore catastrophically fail the element where in
reality the unimpinged volume of material still had a significant
capacity to absorb energy. This has the effect that the results of
analysis based on such techniques do not correlate satisfactorily
with actual experimental results such that they cannot be relied
upon to predict the performance of structures e.g. automotives in
the event of an impact.
This is clearly a serious drawback of conventional techniques and
in practice means that composite materials are not used or in the
few cases where they are used, either the structure must be
sufficiently over-engineered to ensure the required minimum level
of performance, or extensive prototyping and testing is needed in
order to assess performance, which is of course unduly time
consuming and expensive.
There exists a need, therefore, to be able to predict reliably the
performance of composite materials during an impact.
SUMMARY OF THE INVENTION
When viewed from a first aspect the present invention provides a
method of determining the impact resistance of a structure
including a crushable material comprising the steps of determining
for one or more layers of a finite element of said material during
an impact whether said element or layer thereof is to be treated as
failing by crushing; and if said element or layer is determined so
to fail, defining a load-bearing portion of the structure and
treating said load-bearing portion for the purpose of subsequent
calculations as exhibiting an ongoing resistance.
When viewed from a second aspect the invention provides computer
software which, when executed on suitable data processing means,
determines the impact resistance of a structure including a
crushable material by determining for one or more layers of a
finite element of said material during an impact whether said
element or layer thereof is to be treated as failing by crushing
and if said element or layer is determined so to fail, defining a
load-bearing portion of the structure and treating said
load-bearing portion for the purpose of subsequent calculations as
exhibiting a ongoing resistance.
When viewed from a further aspect the invention provides a data
processing apparatus programmed to determine the impact resistance
of a structure including a crushable material, by determining for
one or more layers of a finite element of said material during an
impact whether said element or layer thereof is to be treated as
failing by crushing and if said element or layer is determined so
to fail, defining a load-bearing portion of the structure and
treating said load-bearing portion for the purpose of subsequent
calculations as exhibiting an ongoing resistance.
The inventors have recognised that the actual failure mode of
crushable materials during crush can be approximated as giving an
ongoing resistance throughout the continuous consumption of the
element or layer at the crush front rather than letting the element
or layer as a whole suffer a single rapid failure.
The inventors have realised that the approach in accordance with
the invention gives much more reliable and accurate results in
circumstances where a material undergoes crush.
It should be appreciated that in general the resistive force
returned for the element or layer is not the peak failure stress
but is a somewhat lower value which may be calculated from
materials theory or determined empirically. To give one specific
example, for a typical high strength carbon composite such as T300
in a toughened resin system the compressive failure stress is of
the order of 600 Newtons per square millimeter (N/mm.sup.2).
However, if the material is crushed continually, the resistance to
the impactor is of the order of 100 N/mm.sup.2 i.e. approximately
1/6 of the peak compression strength value.
The invention therefore effectively adds a new failure mode for
elements which are determined to be those which in reality will
undergo crush--i.e. return a resistance force throughout the
consumed length of the element. The crush front may simply be the
forward face of the barrier impacting the structure although this
is not essential and the crush front could instead be defined
elsewhere--e.g. in a fixed relationship relative to the
barrier.
The element or layer which is determined to be failing by crushing
could be deleted, the ongoing resistance being applied to one or
more elements or layers adjacent the deleted element or layer,
and/or another load bearing portion of the structure. Preferably
the load bearing portion is a portion of the element or layer being
crushed itself. For example the element or layer could be resized
or redefined (e.g. by splitting), the ongoing resistance being
distributed across the or each new element or layer. In both of the
foregoing alternatives the barrier is effectively treated as being
impenetratable (save possibly for an allowance for minimal
penetration to avoid computation difficulties at the boundary). The
nodes of the element or layer adjacent to the barrier are therefore
prevented from passing through. However both possibilities are to
be contrasted with conventional finite element in which analysis
rigid barriers are effectively treated as impenetratable and
analysis elements or layers are simply compressed against the
barrier until the failure stress is reached and the element or
layer is deleted with no residual effect.
In presently preferred embodiments of the invention the crush front
is allowed to progress across the element or layer so that the
space occupied by the element or layer "passes through" the crush
front.
The resistance will not in general be a fixed value but rather may
be a function of one or more parameters relating to the element or
layer. In a preferred example the resistance is a function of the
thickness of the element or layer being crushed along the crush
front. Additionally or alternatively the resistance is preferably
dependent upon the contact area at the crush front. Preferably for
a given element the actual value of the resistance force is a
constant function of the contact area. In the simplest case the
resistance force could be directly proportional to the contact area
although this is not essential. Additionally or alternatively where
the crushable material is a composite material, the resistance may
be determined as a function of the lay-up of the layers of the
composite, e.g. the order of the layers.
Furthermore in presently preferred embodiments of the invention the
crush resistance is also a function of one or more dynamic
parameters relating to the impact such as the velocity and/or angle
with which the impactor strikes the element or layer in question or
the amount of rotation imparted to it.
The variations with element/layer and/or dynamic parameters may be
determined by theory, empirically or both. Even if these variations
are determined theoretically, this does not imply that the
corresponding base value is so determined and vice versa. In
practice it is expected that at least the variation of crush
resistance with angle will be empirically determined since this is
very dependent upon the weave of a layer or on each of the layers
of a composite material.
Preferably a set of finite elements of the structure is designated
as being susceptible to crush. The set could comprise all of the
elements in the structure. However the Applicant has realised from
empirical experience that only a relatively small zone of a
composites structure in the immediate vicinity of an impactor will
undergo crash. In preferred embodiments therefore only a subset of
elements is designated as being susceptible to crush, thereby
defining a crush zone. These elements are thus allowed to fail
through the novel crushing mode of the present invention and will
therefore require data allowing their resistance in this failure
mode to be calculated. Elements outside the crush zone will not
have the option of failing by crush. However this means that it is
not necessary to establish data allowing their failure resistance
to be determined. Clearly this is beneficial where empirical data
is used to measure the resistance exhibited during crush since it
obviates the need to establish data for areas outside the crush
zone.
When it is determined in accordance with the invention that a
particular finite element is in the crush regime, the conventional
finite element analysis could simply be suspended in favour of the
novel crush failure mode set out herein--in other words the
conventional finite element analysis calculations would simply not
be carried out for the particular element or layer. In at least
some preferred embodiments however the conventional finite element
calculations are also carried out in parallel so that analysis
reverts to these in the event that at any the element is calculated
to have failed due to another, conventional failure mode such as
shear, tensile or inter-laminar failure at any point whilst the
element is being crushed. To give one example if the crush
resistance force gives rise to very large bending forces an element
might then fail as a result of tensile stress rather than being
crushed.
If the force pushing an element through the crush front is not
sufficient to overcome the resistive force calculated in accordance
with this invention the element can effectively can move back into
conventional finite element analysis. It should be appreciated
however that the element could again pass through the crush front
at a later stage as dictated by the finite element analysis
calculations.
Where analysis reverts to the conventional finite element
calculations the element or layer in question may be deemed
thereafter not to be capable of being crushed or to have a degraded
crush capability. For example the resistance force of the element
or layer in question might be reduced, for the purposes of any
future crush, in proportion to the amount of it which had
previously been `consumed` during the previous crush phase.
Where, as is preferred, the load bearing portion is a portion of
the element or layer being crushed itself, the load bearing portion
could be the whole element or layer, i.e. the resistance force
could conceivably be applied as a distributed force across the
element or layer. However for consistency with normal finite
element analysis it is preferred to apply the force to the
individual nodes of the element so that the nodes comprise the load
bearing portion. In some embodiments the force is divided equally
between the nodes. In other embodiments the force may be biased
towards one or more of the nodes. The force is preferably divided
between nodes that have passed through the crush front and nodes
that have not in proportions according to the amount of the element
by area or penetration distance that has passed through the crush
front. To give an example, if 70% of the element had passed through
the crush front, 70% of the calculated force would be applied to
the nodes that had not yet passed through.
The crush resistance which the element or layer will be treated as
offering may, as mentioned above, be determined using materials
theory. However, the internal mechanisms at work during crush are
often highly complex. For example in fiber composite materials they
depend on inter alia fiber type and sizing, the resin properties,
the cure cycle and the weave style. This complexity is one reason
why attempts to model crush in the past have failed. However, one
of the strengths of the present invention is that it is not
necessary to calculate or even understand the internal mechanisms
responsible since it has been appreciated that for a given set of
macroscopic conditions (area of contact with impactor, velocity,
angle of impact etc.) the crush resistance may be approximated to a
single macroscopic value. This value may therefore be obtained
empirically by performing tests on small samples (known in the art
as "coupons") of the material in question which thereafter allows
it to be modelled in large, complex structures.
In accordance with the invention an element comprising the entire
material thickness could be modelled together or, where the
material comprises layers each layer or sub-group of layers could
be modelled separately.
In accordance with the invention, a determination is made for
analysis elements or layers as to whether or not they are to be
treated as undergoing crush. In embodiments preferred for
simplicity the determination is made by deciding whether the
impactor barrier has physically encroached into the space allocated
to a given element or vice versa. In terms of the model this
amounts to deciding whether any of the element's nodes have "passed
through" the barrier or in other embodiments a crush front defined
in another region of the model space. If failure of the element
through a conventional failure mode has not already taken place,
and the supporting structure has not collapsed, it may then be
deduced that the element will undergo crush. In alternative
embodiments an explicit calculation is made of the stress or strain
on the element which is compared with a threshold failure value.
The element is therefore denoted as being crushed if this threshold
value is exceeded. However the determination is made if an element
is determined to be undergoing crush, the treatment in accordance
with the invention is applied.
It will be appreciated that the ability in accordance with the
invention to model the behaviour of materials being crushed does
not, as has been previously attempted, require drastically reducing
the size of the finite elements used in the model which would in
any event lead to an inordinately large time or computing power
requirement. Rather a practical advantage of using an essentially
continuous model of the crush force, as the methods of the present
invention may be seen, is to allow element sizes which are the same
order of size as would be employed for an equivalent analysis of a
metal structure. This is because when an element has been forced
into the crush regime, as determined in accordance with the
invention, and providing the structure supporting the element in
question is capable of withstanding the forces involved, its edge
length is no longer compressed against the wall of the impactor or
other crush front but is effectively permitted to pass through,
subject, of course, to the resistive force on the wall that the
projected edge length, thickness and crush resistance stress etc.
dictate.
Although in many cases where the principles of the invention are
applied the impactor will be a rigid solid object striking the
structure, this is not essential and the impactor could comprise
another part or body of the structure with sufficient strength and
rigidity.
In presently preferred embodiments shell elements are employed
although alternatively solid or beam or other elements could be
used.
In some embodiments it may be preferred, e.g. for reasons of
computational efficiency, that the relative velocity of the
impactor wall or crush front and the element in question is taken
to be constant during consumption of the element. However, this is
not essential and preferably the relative velocity is adjusted
during the passage of the crush front through the element.
Preferably the resistive force is modified along the length of the
element in accordance with a predetermined function of the relative
velocity.
The same considerations apply to angle dependence to allow for
rotation during consumption of the element. Indeed in general any
parameter on which the crush resistance depends may be updated
during consumption of the element, another example being the
thickness, vibration, temperature etc.
In some preferred embodiments the friction of the crush interface
with the barrier or other crush front may be specified. This is
advantageous as it can influence whether a given element is stable
enough to undergo crush or whether it fails by another
mechanism.
Modelling of the effect of an impact of a structure including a
crushable materials in accordance with the invention may be carried
out without taking damping into account. In some preferred
embodiments however damping coefficients are specified which could
be internal, external or specified globally by the overall finite
element analysis model.
The invention may be applied to any material which can be crushed,
i.e. one which disintegrates with little or no residual strength
under certain conditions. Some possible and non-limiting examples
include concrete, wood, glasses, ceramics, honeycombs and foams. In
preferred embodiments of the invention the crushable material
comprises a composite material, more preferably a
reinforced-reinforced composite material and most preferably a
carbon-fiber reinforced resin.
Although the principles of the invention may be widely applied,
e.g. as part of an original analysis model, preferably software
implementing the invention is incorporated into an existing finite
element modelling package. The type of finite element modelling is
preferably non-linear and could be implicit, explicit or another
type of analysis mathematics, although explicit non-linear analysis
is preferred. In the currently preferred embodiment for example,
the software is incorporated into MSC.Dytran (trade mark) explicit
non-linear finite element analysis software.
BRIEF DESCRIPTION OF THE DRAWINGS
A preferred embodiment of the present invention will now be
described, by way of example only, with reference to the
accompanying drawings in which:
FIG. 1 is a schematic flowchart showing the operation of software
embodying the present invention;
FIG. 2 is a graph showing resistive force against deflection for a
test coupon of a composite material;
FIG. 3 is a graph of deceleration against time for a test cone
which underwent an impact under controlled conditions;
FIG. 4 shows the sled velocity versus displacement for the
experiment of FIG. 3;
FIG. 5 shows the predicted deceleration profile is shown in FIG. 5;
and
FIG. 6 shows the predicted sled velocity.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
In a preferred embodiment of the invention, software operating in
accordance with the principles of the invention is incorporated
into MSC.Dytran (trade mark) 2004 finite element analysis package
which is available from MSC. Software Inc. This known software can
be programmed with failure stress values for composite materials
and thus for a given finite element of the material can attempt to
model the forces on that element until the stress it experiences
exceeds the failure stress whereupon the element is deleted.
However, in the embodiment of the invention now being described,
this part of the functionality of the software is supplemented.
Instead, the process shown in FIG. 1 is followed.
In this process, it is first determined, at 2, when there is impact
between the defined impactor and an element selected as being
capable of crush of the structure. If there is contact, it is
determined, at 4, whether any of the nodes of the element have
penetrated the impactor. If none of the nodes has penetrated the
impactor, the software moves to the next main step at 6 in which
the element stress is updated. However, if penetration is detected,
the software moves, at 7, to assess whether the element connected
to the node is already tagged as undergoing crush. If it is not the
software adds this tag to the node at 8 and then moves on to update
the element stress at 6. If the element connected to the node had
already been tagged as undergoing crush though, a further series of
subroutines is carried out first at 9. Firstly the contact force is
set to zero. Secondly the direction of crush is stored and lastly
the relative velocity is stored.
The next main step at 6 is to update the stress on the element. To
do this it is determined, at 10, how many of the nodes of the
element have been tagged as undergoing crush. If all of the nodes
of the element have been tagged, the element is taken to have
failed and is therefore removed from further calculations at 12. If
one or more, but not all of the nodes is tagged, the software, at
14, projects the crushing direction in the element co-ordinate
system to allow determination of the correct direction for material
properties to be calculated. It then determines the resistance
stress of the element from input data (explained in greater detail
below with reference to FIG. 2) and the whole element is tagged as
undergoing crush.
Alternatively, if at the assessment step 10 none of the nodes is
tagged as undergoing crush, the system simply does nothing, at 16.
Whichever of the possibilities 12, 14, 16 is encountered, the
software then moves to 23 where the conventional finite element
stress update is undertaken prior to moving on to the third main
step of the process in which crushing contact is calculated, at
18.
In this stage, a determination is made, at 20, as to whether the
element has been tagged as undergoing crush. If the element has not
been tagged, processing continues within the previous conventional
analysis mode before returning to the beginning of the process
shown in FIG. 1.
However, if the element has been tagged, four actions are taken.
Firstly, the intersection between the element and the impactor is
calculated. The intersection is calculated to determine the amount
of material being crushed. If a triangle is crushed from a vertex,
the material being crushed will increase and, as a result, the
resistive force will increase as the element is consumed through
the barrier. Secondly, the crush direction is obtained, thirdly the
crush stress is obtained and finally the crush forces are
calculated Thereafter, processing continues within the previous
conventional analysis mode before returning to the beginning of the
process shown in FIG. 1.
In order to calculate the predetermined resistance to be fed into
the model described above, a small coupon of the relevant composite
material is subjected to a crush test. In one example, material
sections of 60.times.30 mm are cut from flat plates and bonded to a
50 mm thick honeycomb sandwich in order to promote stabilized
crush. The outer edges of each skin presented to the impactor are
chamfered at approximately 60.degree. to present a sharp edge to
minimize the spike in crush resistance exhibited at the start of
crushing and thereby minimize the risk of deamination from the
honeycomb at the start of crushing where the initial failure
corresponds to the compressive failure performance of the element.
The honeycomb cells are oriented perpendicular to the direction of
coupon crush and therefore do not absorb significant energy but
ensure that the skins do not buckle. A typical plot of resistance
force exhibited by a coupon versus deflection (i.e. the amount of
the coupon which has been crushed) is shown in FIG. 2. From this it
will be seen that throughout most of the range of deflection the
force is relatively constant. By taking a suitable average value
for this, the resistance force to be used in the analysis model for
a particular material may be determined. Since the coupon has a
constant cross-sectional area, there is no variation of the
resistance force with contact area. However in the model the actual
value of the resistance force is calculated as directly
proportional to the contact length.
It will be appreciated that this method of coupon testing provides
a low cost way of determining the stabilized crush properties for a
wide variety of lay-ups configurations and angles. Thus typically
such tests would be conducted for each of the material
constructions used in the structure to be modelled as crush
capable, and optionally each at a range of angles.
In an exemplary application of the embodiment described, a
rectangular-section cone structure of a T300 carbon fibre composite
material approximately 85.times.115 mm in section and approximately
455 mm long was mounted on a rigid barrier and a rigid sled is
propelled at a controlled velocity into the cone. FIG. 3 shows the
measured deceleration of the trolley versus displacement filtered
using a Butterworth Order4 low pass filter with upper cut-off
frequency of 300 Hz in this experiment (impact occurring at
Displacement=0). From this the actual resistance force encountered
may be calculated simply from the deceleration of the trolley and
its mass. FIG. 4 shows the sled velocity versus displacement for
the same experiment.
The cone was modelled using Dytran 2004 software modified as
described above with reference to FIG. 1. The predicted
deceleration profile is shown in FIG. 5 filtered in the same manner
as the test results, using a Butterworth Order4 low pass filter
with upper cut-off frequency of 300 Hz. From this it will be seen
that the profiles and absolute values of the deceleration are
similar. FIG. 6 shows the predicted sled velocity and here a
remarkable similarity exists between the tested and predicted
results. For example, the prediction of the distance taken to bring
the trolley to a rest was predicted at 327 mm and was measured at
328 mm meaning that the prediction was accurate to within 1%
percent. This is much more accurate than could be achieved with the
prior art methods.
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